Parts and Subword Patterns in Compositions

摘要

We find relationships between subword patterns and residue classes of parts in the set of integer compositions of a given weight. In particular, we show that it is always possible to express the total number of parts in compositions of n that are congruent to i modulo m as a linear combination of the total number of occurrences of subword patterns of length no more than m. We also find an explicit formula enumerating all such parts.